The invention relates to a method for an on the whole minimum-fuel, computer-assisted control of an optionally determined number of thrusters, arranged as desired on a spacecraft, wherein the thrusters can be controlled discretely or continuously.
The use of thrusters is necessary in many situations for exerting external forces and moments on a spacecraft. Since the use of the thrusters requires fuel and this fuel directly influences the starting weight and the service life of the spacecraft, in particular satellites, a thruster control with low total fuel consumption is extremely important. Thruster arrangements, which in principle permit a low fuel consumption, have a higher or equal redundancy with a lower number of thrusters and/or are influenced by the payload on the spacecraft, are frequently irregular and oblique-angled thruster arrangements. For those reasons, the requirement for a minimum-fuel thruster control, particularly also for optional (oblique-angled) fixed thruster arrangements on the spacecraft is particularly relevant.
It is known that the problem of minimum-fuel thruster control can be traced back to a linear optimization problem, for which the simplex algorithm represents a suitable and efficient solution method (e.g., see P. J. Wiktor "Minimum Control Authority Plot: A Tool for Designing Thruster Systems" in: Journal of Guidance, Control, and Dynamics, Vol. 17, No. 5, September-October 1994, pp. 4-5). The use of the simplex algorithm, however, frequently fails because of the required computation time. Thus, the real-time requirements for using the simplex algorithm within the control cycle of the steering and positioning control circuit of a spacecraft, for example, frequently cannot be met because computers that can be used in particular in high orbits cannot process the simplex algorithm with sufficient speed.
Many of the spacecraft (satellites) presently in use are provided with a thruster arrangement where each thruster is arranged parallel to one axis of the body coordinate systems of the spacecraft and thus orthogonal to the other two axes. As a result of this orthogonal and axis-parallel arrangement, each thruster can generate forces only in one axis direction and moments only in one rotational direction around the two other axes. The advantage of this arrangement is that each degree of freedom of the spacecraft as a rigid body can be controlled by using respectively two thrusters only, without influencing other degrees of freedom. Controlling the thrusters with this type of thruster arrangement is very easy. The disadvantage of this thruster arrangement is that at least twelve thrusters are required for the simultaneous and optional control of all degrees of freedom. If the failure of two optional thrusters must be tolerable, then 36 thrusters are required.
In contrast, a suitable oblique-angled thruster arrangement, meaning one that is not orthogonal and axis-parallel, essentially has the following three-point advantage:
1. Less than 12 thrusters are needed for a freely selectable fixed thruster arrangement. PA0 2. Considerably fewer than 36 thrusters are needed for tolerating the failure of two optional thrusters. PA0 3. A lower fuel consumption is possible for a minimum-fuel control of the thrusters. PA0 1. exerts the required forces and moments on the spacecraft, PA0 2. delivers a non-negative control value for each thruster, and PA0 3. minimizes the sum of all control values for the thrusters. PA0 1. exerts the required forces and moments on the spacecraft, PA0 2. delivers a non-negative control value for each thruster, and PA0 3. minimizes the sum of all quadratic control values for the thrusters.
The disadvantage of this thruster arrangement is that the minimum-fuel thruster control requires solving a linear optimization problem and that the computational expenditure for solving this problem with the simplex algorithm frequently is too high. Other methods have therefore been developed, which require less computation time and which make it possible to achieve a more or less minimum-fuel, but on the whole not completely low fuel, thruster control.
With the so-called "linear programming," the thruster control problem is viewed as a linear optimization problem and is solved with relevant methods for the linear optimization, e.g., the simplex algorithm. The previously mentioned disadvantage is the excessively high computation expenditure, which makes it impossible to use this method in many cases.
With the "table look-up method," all minimum-fuel thruster arrangements are computed for the unit forces and the unit moments with respect to one axis of the body coordinate system of the spacecraft (solving of the linear optimization problem) and are stored in a table. In the event that forces and moments must be exerted simultaneously during the operation, the corresponding thruster controls with respect to force or moment are read out of the table for each required axis and the required direction or rotational direction, and are multiplied with the corresponding value for the force component or the moment component in said direction. The control value for each thruster is obtained by adding the individual values for the respective thruster. This method is very simple and quick, but generally does not result in minimum-fuel thruster controls.
The improved and expanded "table look-up" methods are methods for setting up a look-up table containing entries for additionally introduced axes. These methods make it possible to determine fuel-saving thruster controls. At the same time, however, the functional clarity of the method decreases and the computation expenditure increases considerably because of the increasing size of the tables.
Other methods are based on the evaluating and improving the results determined with the "table look-up method." The goal of this evaluation consists in preventing or suitably correcting thruster controls with particularly high fuel consumption. The example to be mentioned in this connection is based on a fuzzy approach (compare T. Suzuki, K. Yasuda, S. Yoshikawa, K. Yamada, N. Yoshida "An Application of Fuzzy Algorithm to Thruster Control Systems of Spacecraft" in: ISTS 94-c-16, 19.sup.th International Symposium on Space Technology and Science, Yokohama, Japan, May 15-24, 1994, pp. 1-8).
The goal of minimizing the fuel consumption on the whole is to determine a thruster control, which
As previously mentioned, this represents a linear optimization problem. Since solving the problem as a rule is too time-consuming, the quadratic optimization problem can be solved as a substitution problem.
The solution of the substitution problem leads to a determination of that thruster control, which
This quadratic optimization problem can be solved by providing the Moore-Penrose-inverted system matrix for the thruster arrangement on the spacecraft and an offset vector, which is computed with the aid of the singular value factoring (e.g. compare B. Noble, I. W. Daniel "Applied linear algebra" Prentice Hall International, INC. (1988), pp. 338-350). The solution for the quadratic optimization problem is then obtained as product of the Moor-Penrose inverted system matrix with the commanded forces-moments vector and the addition of the offset vector. Adding the offset vector means that only non-negative control values occur in the solution vector. However, computing the offset vector becomes numerically more and more involved if the number of thrusters to be controlled exceeds the dimension of the commanded forces-moments vector by two or more. The solution is generally not a minimum-fuel solution, but coincides with the solution for the linear optimization problem if the number of thrusters to be controlled exceeds the dimension of the commanded forces-moments vector by only one (e.g., compare DE 195 19 732 A1). A further disadvantage is that longer operating times are "penalized" disproportionally and therefore occur less often in the controls. However, it is better for the operation of the thrusters and their degree of effectiveness if they are operated for longer periods of time.
Existing methods therefore have the disadvantage that they either do not solve the linear optimization problem and thus generally do not provide the minimum-fuel control of the thrusters, or that the computation effort required for solving the linear optimization problem of the control methods is generally too high if the simplex algorithm is used.
It is the object of the invention to provide a method of the aforementioned type, with which the linear optimization problem for the minimum-fuel control of optionally fixed thruster arrangements, for a simultaneous realization of forces and moments on a spacecraft, can be solved in a significantly shorter time period than has been possible so far.